Mathematical Sciences: Microlocal Character Theory for Representations of Classical Lie Groups

Przebinda将在Howe的约化对偶理论背景下，通过Cayley变换，从微局部分析的角度研究经典李群的不可约酉表示的分布特征和矩阵系数。将利用Howe的理论、微局部分析和Harish-Chandra的轨道积分理论来构造经典李群的不可约酉表示，这些李群连接到幂零共伴轨道上。这种依恋发生在三个层次上：相关的品种、波前集和字符公式。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。* * / /

Przebinda will investigate distribution characters and matrix coefficients of irreducible unitary representation of classical Lie groups from the viewpoint of microlocal analysis in the context of Howe's theory of reductive dual pairs, via the Cayley transform. Use will be made of Howe's theory, microlocal analysis, and Harish-Chandra's theory of orbital integrals to construct irreducible unitary representations of classical Lie groups, attached to nilpotent coadjoint orbits. This attachment occurs on three levels: associated varieties, wave front sets, and character formulas. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics. **//